A cable that weighs 8 lb/ft is used to lift 900 lb of coal up a mine shaft 450 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)

Given :

Work done by a segment dx of a cable :

dW = 8dx x = 8x dx

So, work done by whole cable :

Now, work done to bring coal up :

Therefore, total work done is ( 810000 + 405000 ) = 1215000 ft-lb .

Hence, this is the required solution.

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step-by-step explanation: